Abstract
In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβ- open sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the characterizations for the intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are obtained. The relationships between intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are discussed. Finally, we prove the irresoluteness in (i,j)–πgβ intuitionistic fuzzy bitopological spaces.
Highlights
The notion of β-open set was introduced by Abd ElMonsef et al [1] and Andrijevic [2]
In 2012, the notion of bitopological space was introduced in intuitionistic fuzzy topology by - Jin Tae Kim, Seok Jong Lee [6]
The concepts of πgβ-closed set have been extended to the bitopological spaces in intuitionistic fuzzy topology and we introduce a new form of closed set called Intuitionistic fuzzy (IF) (i,j)-πgβ-closed set., The notion of IF (i,j)- πgβ -continuous function and irresolute function is introduced and studied
Summary
The notion of β-open set was introduced by Abd ElMonsef et al [1] and Andrijevic [2]. The concept of bitopological spaces (X,τi,τj) was introduced by Kelly J. As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by Atanassov [3]. Kandil [7] introduced the concept of fuzzy bitopological spaces as a natural generalization of Chang’s fuzzy topological spaces. In 2012, the notion of bitopological space was introduced in intuitionistic fuzzy topology by - Jin Tae Kim, Seok Jong Lee [6]. The concepts of πgβ-closed set have been extended to the bitopological spaces in intuitionistic fuzzy topology and we introduce a new form of closed set called Intuitionistic fuzzy (IF) (i,j)-πgβ-closed set., The notion of IF (i,j)- πgβ -continuous function and irresolute function is introduced and studied
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